A176151 - OEIS

%I #15 Feb 08 2021 05:16:35

%S 1,1,1,1,6,1,1,9,9,1,1,27,26,27,1,1,105,118,118,105,1,1,613,706,714,

%T 706,613,1,1,4333,4930,5016,5016,4930,4333,1,1,35297,39610,40208,

%U 40278,40208,39610,35297,1,1,322577,357856,362168,362742,362742,362168,357856,322577,1

%N Triangle T(n, k) = 2*(n+1 - mod(n, k+1) - mod(n, n-k+1) ) + (n! - k! - (n-k)!) read by rows.

%C Row sums are: 1, 2, 8, 20, 82, 448, 3354, 28560, 270510, 2810688, 31841122, ...

%H G. C. Greubel, <a href="/A176151/b176151.txt">Rows n = 0..100 of the triangle, flattened</a>

%F T(n, k) = 2*(n+1 - mod(n, k+1) - mod(n, n-k+1) ) + (n! - k! - (n-k)!).

%F T(n, k) = 2*A176149(n, k) - A155170(n, k). - _G. C. Greubel_, Feb 07 2021

%e Triangle begins as:

%e   1;

%e   1,      1;

%e   1,      6,      1;

%e   1,      9,      9,      1;

%e   1,     27,     26,     27,      1;

%e   1,    105,    118,    118,    105,      1;

%e   1,    613,    706,    714,    706,    613,      1;

%e   1,   4333,   4930,   5016,   5016,   4930,   4333,      1;

%e   1,  35297,  39610,  40208,  40278,  40208,  39610,  35297,      1;

%e   1, 322577, 357856, 362168, 362742, 362742, 362168, 357856, 322577, 1;

%t Table[2*(n+1 -Mod[n, k+1] -Mod[n, n-k+1]) + (n! -k! -(n-k)!), {n, 0, 10}, {k, 0, n}]//Flatten

%o (Sage) f=factorial; flatten([[2*(n+1 - n%(k+1) - n%(n-k+1)) + (f(n) -f(k) -f(n-k)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Feb 07 2021

%o (Magma) F:=Factorial;; [2*(n+1 - n mod (k+1) - n mod (n-k+1)) + (F(n) -F(k) -F(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Feb 07 2021

%Y Cf. A155170, A176149.

%K nonn,tabl,easy,less

%O 0,5

%A _Roger L. Bagula_, Apr 10 2010

%E Edited by _G. C. Greubel_, Feb 07 2021